This paper criticizes non-constructive uses of set theory in formal economics. The main focus is on results on preference aggregation and Arrow’s theorem for infinite electorates, but the present analysis would apply as well, e.g., to analogous results in intergenerational social choice. To separate justified and unjustified uses of infinite populations in social choice, I suggest a principle which may be called the Hildenbrand criterion and argue that results based on unrestricted axiom of choice do not meet this criterion. The (...) technically novel part of this paper is a proposal to use a set-theoretic principle known as the axiom of determinacy ), not as a replacement for Choice, but simply to eliminate applications of set theory violating the Hildenbrand criterion. A particularly appealing aspect of \ from the point of view of the research area in question is its game-theoretic character. (shrink)

We prove that all finitely axiomatizable tense logics with temporal operators for ‘always in the future’ and ‘always in the past’ and determined by linear fows time are coNP-complete. It follows, for example, that all tense logics containing a density axiom of the form ■n+1F p → nF p, for some n ≥ 0, are coNP-complete. Additionally, we prove coNP-completeness of all ∩-irreducible tense logics. As these classes of tense logics contain many Kripke incomplete bimodal logics, we obtain many natural (...) examples of Kripke incomplete normal bimodal logics which are nevertheless coNP-complete. (shrink)

In this paper, we are going to analyze the phenomenon of modal incompleteness from an algebraic point of view. The usual method of showing that a given logic L is incomplete is to show that for some L and some cannot be separated from by a suitably wide class of complete algebras — usually Kripke algebras. We are going to show that classical examples of incomplete logics, e.g., Fine logic, are not complete with respect to any class of complete BAOs. (...) Even above Grz it is possible to find a continuum of such logics, which immediately implies the existence of a continuum of neighbourhood-incomplete Grz logics. Similar results can be proved for Löb logics. In addition, completely incomplete logics above Grz may be found uniformly as a result of failures of some admissible rule of a special kind. (shrink)

In this article, we tell a story about incompleteness in modal logic. The story weaves together an article of van Benthem, “Syntactic aspects of modal incompleteness theorems,” and a longstanding open question: whether every normal modal logic can be characterized by a class of completely additive modal algebras, or as we call them, ${\cal V}$-baos. Using a first-order reformulation of the property of complete additivity, we prove that the modal logic that starred in van Benthem’s article resolves the open question (...) in the negative. In addition, for the case of bimodal logic, we show that there is a naturally occurring logic that is incomplete with respect to ${\cal V}$-baos, namely the provability logic $GLB$. We also show that even logics that are unsound with respect to such algebras do not have to be more complex than the classical propositional calculus. On the other hand, we observe that it is undecidable whether a syntactically defined logic is ${\cal V}$-complete. After these results, we generalize the Blok Dichotomy to degrees of ${\cal V}$-incompleteness. In the end, we return to van Benthem’s theme of syntactic aspects of modal incompleteness. (shrink)

In this paper, we introduce an extension of the modal language with what we call the global quantificational modality [∀p]. In essence, this modality combines the propositional quantifier ∀p with the global modality A: [∀p] plays the same role as the compound modality ∀pA. Unlike the propositional quantifier by itself, the global quantificational modality can be straightforwardly interpreted in any Boolean Algebra Expansion (BAE). We present a logic GQM for this language and prove that it is complete with respect to (...) the intended algebraic semantics. This logic enables a conceptual shift, as what have traditionally been called different “modal logics” now become [∀p]-universal theories over the base logic GQM: instead of defining a new logic with an axiom schema such as □φ→□□φ, one reasons in GQM about what follows from the globally quantified formula [∀p](□p→□□p). (shrink)

This paper provides several examples of how modal logic can be used in studying the XML document navigation language XPath. More specifically, we derive complete axiomatizations, computational complexity and expressive power results for XPath fragments from known results for corresponding logics. A secondary aim of the paper is to introduce XPath in a way that makes it accessible to an audience of modal logicians.

Argues that the key distinction between human and nonhuman social cognition consists in our complex, diverse and flexible capacities to shape each other's minds in ways that make them easier to interpret.

Argues that the key distinction between human and nonhuman social cognition consists in our complex, diverse and flexible capacities to shape each other's minds in ways that make them easier to interpret.

The article presents two concepts of indexicality. The first, more standard and narrow, identifies indexicality with systematic (meaning controlled) context-sensitivity. The second, broader (derived from the work of Jerzy Pelc), conceives indexicality in terms of the potential variability of the general semiotic characteristics expressions (with respect to the context of use). The text introduces the concept of a pragmatic matrix that serves for a schematic representation of contextual variation. I also recapitulate briefly the views of Jerzy Pelc on the meaning (...) (manner of use) and use of expressions, and briefly indicate its relationship approaches with contemporary debates around contextualism and status of non-sentential speech acts. Finally, the relationship between the broader notion of indexicality and the directival theory of meaning is analyzed. (shrink)

This is a new edition of the manual published in 1974 and 1984. Compared with those earlier editions it is revised, enlarged and more precise in its argumentation. In its beginnings the manual aimed at meeting the didactic needs to present students of the Faculty of Christian Philosophy at the ATK a complete handling of Christian ethics. The author, who wrote his manual in difficult times of communist ideology, decided to include in one work, besides a positive exposition of Christian (...) ethics, a critical discussion with other ethical systems as well as his own explicit theory on Augustinian and Thomistic ethics, which he endeavoured to develop. Thus the work interlocked the didactic objectives and the process of growth and justification of the Author's views, Krakow 2001, p. 308). (shrink)

When it comes to social criticism of the economy, Critical Theory has thus far failed to discover specific immanent norms in that sphere of activity. In response, we propose that what is needed is to double down on the idealism of Critical Theory by taking seriously the sophisticated structure of agency developed in Hegel’s own account of freedom as self-determination. When we do so, we will see that the anti-metaphysical gestures of recent Critical Theory work in opposition to its attempts (...) to develop immanent critique. In this paper we first briefly reconsider Axel Honneth’s project as it concerns economic institutions and then respond by returning to the problem of freedom and articulating a view according to which the problem of individual self-determination and the problem of social production are the same problem seen from different angles. Then we present briefly Hegel’s own social theory from this perspective before moving on to trace the outlines of such a critical theory of contemporary capitalism. (shrink)

I argue for two claims. First I argue against the consensus view that accurate behavioral prediction based on accurate representation of cognitive states, i.e. mind reading , is the sustaining function of propositional attitude ascription. This practice cannot have been selected in evolution and cannot persist, in virtue of its predictive utility, because there are principled reasons why it is inadequate as a tool for behavioral prediction. Second I give reasons that favor an alternative account of the sustaining function of (...) propositional attitude ascription. I argue that it serves a mind-shaping function. Roughly, propositional attitude ascription enables human beings to set up regulative ideals that function to mold behavior so as to make it easier to coordinate with. (shrink)

Maximilian de Gaynesford has argued against the standard view that the reference of the first-person pronoun ‘I’ is determined by a rule linking the referent to some feature of the context of use. In this paper, we argue that de Gaynesford's arguments are inconclusive. Our main aim, however, is to formulate a novel version of the reference rule for ‘I’. We argue that this version can deal with several problematic cases. Our strategy involves analysing the so-called agent of the context (...) as the person responsible for a particular speech act. From this analysis, we exclude a particular class of uses of ‘I’, uses that we believe are best understood as demonstrative. (shrink)

A set-theoretical proof of Gowers’ Dichotomy Theorem is presented together with its application to another dichotomy concerning asymptotic l 2 basic sequences.

L’autodeterminazione è una categoria fondamentale nella visione personalistica di K. Wojtyła. Essa è una relazione entro la volontà. Una relazione di cui si potrebbe dire: la volontà si rivela come proprietà della persona e la persona come realtà che, riguardo al suo dinamismo, è constituita propriamente dalla volontà. L’autodeterminazione non è un atto chiuso entro se stesso, preché essenziale è il momento della verità e nella verità.

Artykuł omawia postać Jerzego Grobickiego, który służył jako oficer armii cesarsko-królewskiej i został pułkownikiem Wojska Polskiego w II RP. Brał udział w I i II wojnie światowej, a po wojnie wyemigrował do Kanady.

I review recent evidence that very young, pre-verbal infants attribute belief-like states when anticipating the behavior of others. This evidence is drawn from infant performance on non-verbal false belief tasks. I argue that, contrary to typical interpretations, such evidence does not show that infants attribute belief-like states. Rather, it shows that infants apply an enhanced version of what Gergely ( 2011 ) calls the “teleological stance” to brief bouts of behavior. This requires them to parse behavioral sequences into goals and (...) rationally/informationally-constrained means of achieving them; however, it does not require the attribution of unobservable mental states, like beliefs, that are causally responsible for behavior. (shrink)